Decomposition of signals into a sum of truncated fourier series

Abstract

Systems and methods of performing decomposition of baseband and bandpass signals into a sum of time truncated periodic components with spectral masks defined by the set of Fourier coefficients of the components and the pulse used for time truncation are provided. In one exemplary embodiment, a user equipment device includes a circuitry operable to output a set of truncated periodic components that collectively represents a sample of an input signal having information and a set of power amplifier circuitry electrically coupled to the circuitry and operable to amplify the set of truncated periodic components that collectively represents an amplified sample of the input signal.

What is claimed is: 
     
       1. A method, comprising:
 generating, by a circuitry, a set of periodic components based on a set of quantization bits that represents a quantized amplitude of a sample of an input signal having information and a set of periodic component activation indications that indicates which of the set of periodic components is activated or deactivated; 
 outputting, by the circuitry, a set of truncated periodic components that collectively represents the input signal sample; and 
 amplifying, by a set of power amplifier circuitry electrically coupled to the circuitry, the set of truncated periodic components that collectively represents an amplified sample of the input signal. 
 
     
     
       2. The method of  claim 1 , further comprising:
 computing an amplitude and a phase of the sample; 
 quantizing the amplitude to obtain the set of quantization bits that represents the quantized amplitude of the sample; and 
 decomposing the set of quantization bits that represents the quantized amplitude of the sample to obtain the set of periodic component activation indications that indicates which of the set of periodic components is activated or deactivated. 
 
     
     
       3. The method of  claim 1 , further comprising:
 truncating the set of periodic components to a certain sample period to obtain the set of truncated periodic components. 
 
     
     
       4. The method of  claim 1 , further comprising:
 combining the amplified set of truncated periodic components to obtain an output signal. 
 
     
     
       5. A user equipment device, comprising:
 a circuitry operable to:
 generate a set of periodic components based on a set of quantization bits that represents a quantized amplitude of a sample of an input signal having information and a set of periodic component activation indications that indicates which of the set of periodic components is activated or deactivated; and 
 output a set of truncated periodic components that collectively represents the input signal sample; and 
 
 a set of power amplifier circuitry electrically coupled to the circuitry and operable to amplify the set of truncated periodic components that collectively represents an amplified sample of the input signal. 
 
     
     
       6. The device of  claim 5 , further comprising:
 a first circuitry operable to compute an amplitude and a phase of the sample; 
 a second circuitry operable to quantize the amplitude to obtain the set of quantization bits that represents the quantized amplitude of the sample; and 
 a mapper circuitry operable to decompose the set of quantization bits that represents the quantized amplitude of the sample to obtain the set of periodic component activation indications that indicates which of the set of periodic components is activated or deactivated. 
 
     
     
       7. The device of  claim 5 , further comprising:
 a truncation circuitry operable to truncate the set of periodic components to a certain sample period to obtain the set of truncated periodic components. 
 
     
     
       8. The device of  claim 5 , further comprising:
 a combiner circuitry operable to combine the amplified set of truncated periodic components to obtain an output signal. 
 
     
     
       9. A method, comprising:
 generating, by a circuitry, a set of periodic components based on a set of quantization bits that represents a quantized amplitude of a sample of an input signal having information and a set of periodic component activation indications that indicates which of the set of periodic components is activated or deactivated; and 
 amplifying, by a set of power amplifier circuitry, a set of truncated periodic components that collectively represents an amplified sample of the input signal. 
 
     
     
       10. The method of  claim 9 , further comprising:
 computing an amplitude and a phase of the sample; 
 quantizing the amplitude to obtain the set of quantization bits that represents the quantized amplitude of the sample; and 
 decomposing the set of quantization bits that represents the quantized amplitude of the sample to obtain the set of periodic component activation indications that indicates which of the set of periodic components is activated or deactivated. 
 
     
     
       11. The method of  claim 9 , further comprising:
 truncating the set of periodic components to a certain sample period to obtain the set of truncated periodic components. 
 
     
     
       12. The method of  claim 9 , further comprising:
 combining the amplified set of truncated periodic components to obtain an output signal. 
 
     
     
       13. A user equipment device, comprising:
 a circuitry operable to generate a set of periodic components based on a set of quantization bits that represents a quantized amplitude of a sample of an input signal having information and a set of periodic component activation indications that indicates which of the set of periodic components is activated or deactivated; and 
 a set of power amplifier circuitry operable to amplify a set of truncated periodic components that collectively represents an amplified sample of the input signal. 
 
     
     
       14. The device of  claim 13 , further comprising:
 a first circuitry operable to compute an amplitude and a phase of the sample; 
 a second circuitry operable to quantize the amplitude to obtain the set of quantization bits that represents the quantized amplitude of the sample; and 
 a mapper circuitry operable to decompose the set of quantization bits that represents the quantized amplitude of the sample to obtain the set of periodic component activation indications that indicates which of the set of periodic components is activated or deactivated. 
 
     
     
       15. The device of  claim 13 , further comprising:
 a truncation circuitry operable to truncate the set of periodic components to a certain sample period to obtain the set of truncated periodic components. 
 
     
     
       16. The device of  claim 13 , further comprising:
 a combiner circuitry operable to combine the amplified set of truncated periodic components to obtain an output signal.